Problem 2:

 Sides of a triangle

You are given a positive integer array sides of length 3.

Determine if there exists a triangle with positive area whose three side lengths are given by the elements of sides.

If such a triangle exists, return an array of three floating-point numbers representing its internal angles (in degrees), sorted in non-decreasing order. Otherwise, return an empty array.

Answers within 10-5 of the actual answer will be accepted.

Example 1:

Input: sides = [3,4,5]

Output: [36.86990,53.13010,90.00000]

Explanation:

You can form a right-angled triangle with side lengths 3, 4, and 5. The internal angles of this triangle are approximately 36.869897646, 53.130102354, and 90 degrees respectively.

Example 2:

Input: sides = [2,4,2]

Output: []

Explanation:

You cannot form a triangle with positive area using side lengths 2, 4, and 2.

Constraints:

• sides.length == 3

• 1 <= sides[i] <= 1000

class Solution {

    public double[] internalAngles(int[] sides) {

        Arrays.sort(sides);

        if (sides[0] + sides[1] > sides[2] &&

            sides[1] + sides[2] > sides[0] &&

            sides[0] + sides[2] > sides[1]) {

            double A = angleFromSides(sides[1], sides[2], sides[0]);

            double B = angleFromSides(sides[0], sides[2], sides[1]);

            double C = angleFromSides(sides[0], sides[1], sides[2]);

            double[] angles = {A, B, C};

            Arrays.sort(angles); // non-decreasing order

            return angles;

        } else {

            return new double[0];

        }

    }

    private static double angleFromSides(int side1, int side2, int opposite) {

        double numerator = (side1 * side1) + (side2 * side2) - (opposite * opposite);

        double denominator = 2.0 * side1 * side2;

        double cosValue = numerator / denominator;

        // Numerical safety: clamp to [-1, 1]

        cosValue = Math.max(-1.0, Math.min(1.0, cosValue));

        return Math.toDegrees(Math.acos(cosValue));

    }

}

Test cases:

Case 0:

Input

sides =

[3,4,5]

Output

[36.86990,53.13010,90.00000]

Expected

[36.86990,53.13010,90.00000]

Case 1:

Input

sides =

[2,4,2]

Output

[]

Expected

[]